Create Arcs tangent to 3D Surface

I'm trying to find a method to create arcs that are tangent to a 3D Surface.

For example, say the curve in the picture to which all the catenary arcs are tangent, is the cross section of a 3D surface. I want to project a grid of points on to the surface, and then apply tangent arcs (in this case Catenary arcs) to the surface at each grid point.

Any suggestions on how to do this?

Replies to This Discussion

Permalink Reply by Fred Becquelin on November 13, 2012 at 3:50pm

Something like this :

U and V are colinear if U.V=1

Let U be the fist tangent vector on the cross section

and V(t) a list of tangent vectors along the arc, t being the respective parameter (what we want).

So I can plot U.V(t) and graphically solve it with the curve extremes component to find t.

Attachments:

Tangent Arcs.3dm, 25 KB
Tangent Arcs.gh, 9 KB

Permalink Reply by Bret Vanderhyden on November 14, 2012 at 2:31pm

thanks for this. There's some interesting stuff going on here. I am definitely going to spend some time dissecting the definition. Thanks

-Bret

Permalink Reply by Bret Vanderhyden on November 16, 2012 at 4:00pm

this is really cool. You get a really cool graphical representation of the vector dot product when the curve is reparameterized to 0-1.

Permalink Reply by Fred Becquelin on November 19, 2012 at 3:25am

Indeed I like this method vert much, you can apply it to a lot of problems...

Permalink Reply by Bret Vanderhyden on November 19, 2012 at 9:54am

thanks for your help

Permalink Reply by Benjamin Felbrich on November 19, 2012 at 11:15am

wow,

i had the same issue once, but you solved in a much smoother way. cool.
i used galapagos to find exactly the L-value of the catenary, with which the curves (catenary and section curve) "kiss" in one point.

Benjamin

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